Special Issue on the nano devices 서울대 나노 협동과정& 나노 응용시스템 연구센터(NSI_NCRC) The 2nd lecture: MOS operational principle Prof. Young June Park

Syllabus (updated) - 나노 물리소자 특강 부제“ 한글; 나노반도체와 분자소자 결합 목요일 오후 1시-4시 교수학습개발센터 1층 스튜디오 강의실 전기신호를 이용해서 신호 및 에너지를 변환하거나, 전환하는 소자가 나노 분야에서 사용되고 있다. 빛, 화학, 분자와 전자소자의 interaction 등에 대해서 콜로키움 형태로 특강을 진행한다.

Syllabus (updated) 1. Introduction: motivation of the lecture         1주: 박 영준교수 2. Nano semiconductor Device operational principle         2주(3/14): MOSFET operational principle(박 영준교수)         3주(3/22): 1. IV characteristics of MOSFET(박 영준교수)               2,3: Nanowire MOSFET(박병국교수)     4주(3/29): Single Electron Transistor and its molecular interaction              (박 병국, 박영준교수)

Syllabus (updated) 3. Lecture from Max Plank(Germany): Dr. S. Roth         5주(4/5):  Introduction into the physics of low-dimensionsal materials:         6주(4/12) Conducting Polymers         7주(4/19) Carbon Nanotubes         8주(4/26) Graphene Layers         4:30~6:00           교재:  VCH: One dimensional conductor available from http://www.wiley-vch.de/publish/en/books/ISBN3-527-30749-4/ http://www.amazon.com/One-Dimensional-Metals-Physics-Materials-Science/dp/3527268758     8주 : review and midterm

Syllabus (updated) 4. 전기화학의 기초( 성영은교수) 9주(5/3): 전기화학의 기초         9주(5/3):   전기화학의 기초         10주(5/10): characterization techniques (cyclo voltametry) - may be shifted to 9th         11주(5/17): Electric double layer structure                     Faradaic interface                    Non Faradaic interface

Syllabus (updated) 5. ISFET and molecule-insulator surface         5. ISFET and molecule-insulator surface         12주(5/31) ISFET: Molecular and insulator interface (박영준교수)         13주(6/7):  molecule to insulator(electrode) interface(강헌교수)          6. Others         14주(6/14) :          1. Charge transport in Organic device(이창희교수)

MOS equation and CV characteristics MOS eq:quantum and classical model C-V characteristics Long channel IV characteristics Ref :  Y.J.Park, B.G.Park, H.C. Shin, H.S.Min, VLSI device with NANOCAD, chapter 2, (Korean) Grove, Chap. 4, Physics and Technology of Semiconductor Dev., John Wiley & Sons, 1967

MOS Equations(1) (1) describes the voltage across the gate, oxide and semiconductor surface with respect some references   is when so that is called "the Flat Band Voltage" : voltage applied in the gate caused by the poly depletion effect : voltage applied across the oxide : Semiconductor surface potential w,r,t some reference voltage (see next page for the reference)

MOS Equations(2) Find the relation , with a single variable , From simple D continuity consideration between interfaces; Gate- oxide and oxide semiconductor interface, Vox = QG/Cox ( notice that Qs=-QG due to charge conservation) Find the relation , with a single variable , then we can solve the MOS equations with respec to . This can be achieved by using the "semiconductor areal charge density", represented by Vox (so ) Ex) Draw the rho(****) and field relation in the depth direction as you did in the case of PN junction.

Qs and relationships There are several models to find Qs and relationships - classical with MB statistics - classical with FD statistics - Quantum mechanical model

relationship: classical model Assuming that the surface is not quantized in x direction, and MB statistics is valid, the general relation can be found as,                                (2)     where               Then            (from the continuity in electric flux, D) (3)     and                                                 (4)

Vertical Electric Fields Important physical quantities related with vertical fields                                                : Es and Eox, and Eeff Eox : determines the tunneling current in thin oxide,  limiting the minimum thickness of gate oxide. Eeff : determines the effective vertical field which carriers see in vertical direction. Ex) relationship     Draw relationship from Eq. (1)

Classical VT theory is value in which is appreciable so that drain current is detectable. Eq.(2) states that is exponentially increasing function of whereas is increasing function in the power of 0.5. So, as we do approximate I-V of diode such that I=0 when where is around 0.7V even though I flows continuously as increases from 0V, we assume that until becomes a certain value ( ). Also assume that is fixed to the value and does not increase further. With this assumptions, classical expression for  MOS VT and can be found.

Classical VT theory(2) Assume , for , Eq. (1) becomes, so that where .          so that      where .      For , since is fixed to Eq.(1) becomes,      so after inversion can be written found as,    . 

Subthreshold characteristics

Subthreshold characteristics(VGS vs. )

Subthreshold characteristics

quantum mechanical model Eq. For Qn for 2 D gas as function of Ei and Ef. Schrodinger eq. For Ei and the Poisson equation for Vp Equation for n(x): n(x) determines Vp => Ei and Ni(Qn)

quantum mechanical model

C-V Characteristics One of the most powerful experimental method to know the MOS surface is measurement of gate capacitance CG vs VG. Here, DC VG is applied and a small signal is applied with a certain frequency so that the current through the gate is measured and transformed to Capacitance. DC VG is scanned so that C-VG can be plotted.

C-V Characteristics(2) The applied frequency is so low that the electron concentration can be responded so that Eq. (1) with relation always hold. If high frequency is applied so that electron cannot be responded to the applied signal, high frequency characteristics is observed. Differentiating Eq.(1) with respect to ,

C-V Characteristics(3) Notice that this Eq. can be written as

C-V Characteristics Above Fig. shows that approximate Cs behavior. The following feature should be noticed. and . Notice that from , can be found, so the  Then can be obtained from .

C-V Characteristics(4) Let us first consider Cs.  From Eq. (2), Cs can be easily found as, Fig. 2 shows that approximate Cs behavior. The following feature should be noticed. and . Notice that from , can be found, so be .  Then can be obtained from .

From C. Richter's, EDL p.35, Jan 2001) Effects of quantum mechanical model on CV From C. Richter's, EDL p.35, Jan 2001)

1-1. MOSFET current : General Band diagram VGS VS VDS y VBS x

1-2.Classical approximation above threshold Above threshold, current is mainly due to the drift.                        

Classical approximation  above threshold

Classical approximation above threshold (pinch off voltage) The equation for VDS,sat due to pinch off is

1-3. below threshold (Subthreshold characteristics) Current in the subthreshold region is assumed to be due to diffusion,

Classical approx. below threshold (Subthreshold characteristics) Now the relationship between and VGS-VT is,

Classical approx. below threshold (Subthreshold characteristics)

1-4. Mobility in the inversion layer S. Takaki et. al, "On the universality of inversion layer                 mobility in N- and P- channel MOSFET's," IEDM,                 pp.398-401, 1988.

Mobility enhancement Enhancement of the MOS mobility is one of the key Issues to enhance the CMOS circuit performance. Lowering the vertical field Using the strained layer to change the effective mass Stress induced mobility change is used as the molecular sensor.

Mobility enhancement( from Tagaki, IEDM short lecture , 2003) Using the strained layer to change the effective mass. [5] J. J. Welser, J. L. Hoyt and J. F. Gibbons, IEDM Tech. Dig., 1000 (1992)

Mobility Enhancement